Twenty-seven people were killed and 40 injured on Tuesday in a stampede in the Indian state of Andhra Pradesh, police said, as crowds surged to bathe in the Godavari River on the first day of a religious festival held once every 144 years.

Twenty-six women and one man died and at least 40 pilgrims were injured in the crush, said police deputy superintendent B. Ramakrishna of Rajahmundry district, where the festival is held.

The stampede started after a woman fell down in a crowd pushing to get through a narrow entrance to the banks of the Godavari, he said.

Police estimated the crowd swelled to more than one million on Tuesday. The government of the southern state expects some 40 million pilgrims to attend the Godavari Maha Pushkaralu, a Hindu festival held at the banks of the holy river to offer prayers over the next 12 days.

Stampedes are not uncommon at India's large religious festivals, where crowds routinely number in the tens of millions. In 2013, 36 pilgrims were killed during a stampede in a train station during a festival in northern India.

Prime Minister Narendra Modi expressed his condolences to the victims' families.

"Deeply pained at the loss of lives due to stampede at Rajahmundry," Modi said in a statement. "My condolences to the families of the deceased and prayers with the injured."

Andhra Pradesh Chief Minister Chandrababu Naidu, who took a dip in the river earlier in the day to kick off festivities, announced a sum of one million rupees ($15,750), in compensation for each victim's family.

He also ordered the deployment of more police to help control the crowds, Naidu's office said.

More than 15,000 police and 171 closed circuit television cameras were already in place to monitor the flow of visitors to the festival, officials said.

The incident did not deter pilgrims, who continued to pour into the festival grounds, carrying children and luggage above their heads or perched atop cars stranded in the throng.

The Maha Pushkaralu is one of India's largest Hindu festivals, held once in 144 years to worship the Godavari River in the states of Andhra Pradesh and Telangana.